In the SM, the various transition form factors in Eqs. (REF ), (REF ) and (REF ) are mainly governed by the nonperturbative strong interactions. Although chiral perturbation theory can be used to reliably calculate the form factors in the very low energy region around the thresholds, it becomes inadequate in the energy region where hadron resonances start to contribute. Alternatively, resonance chiral theory (R\(\chi \) T) [1]}, [2]}, which explicitly includes the bare resonance fields in a chiral covariant way, offers a reliable theoretical framework to calculate the form factors both in the low and resonant energy regions. Indeed R\(\chi \) T has been widely employed to investigate many phenomenological processes involving the light-flavor hadron resonances, including the meson-meson scattering [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, the hadronic \(\tau \)  decays [9]}, [10]}, [11]}, [12]}, [13]}, the form factors [14]}, [15]}, the hadronic and radiative decay processes of various hadrons [16]}, [17]}, [18]}, [19]}, etc. We further proceed the applications of the R\(\chi \) T to calculate the form factors appearing in the \(\tau \rightarrow \pi \pi \gamma \nu _\tau \)  process.
